Node centrality measures are a poor substitute for causal inference

Fabian Dablander,Max Hinne

doi:10.1038/s41598-019-43033-9

Abstract

Network models have become a valuable tool in making sense of a diverse range of social, biological, and information systems. These models marry graph and probability theory to visualize, understand, and interpret variables and their relations as nodes and edges in a graph. Many applications of network models rely on undirected graphs in which the absence of an edge between two nodes encodes conditional independence between the corresponding variables. To gauge the importance of nodes in such a network, various node centrality measures have become widely used, especially in psychology and neuroscience. It is intuitive to interpret nodes with high centrality measures as being important in a causal sense. Using the causal framework based on directed acyclic graphs (DAGs), we show that the relation between causal influence and node centrality measures is not straightforward. In particular, the correlation between causal influence and several node centrality measures is weak, except for eigenvector centrality. Our results provide a cautionary tale: if the underlying real-world system can be modeled as a DAG, but researchers interpret nodes with high centrality as causally important, then this may result in sub-optimal interventions.

Highlights

In the last two decades, network analysis has become increasingly popular across many disciplines dealing with a diverse range of social, biological, and information systems
It has been shown that alterations in brain network structure can be predictive of disorders and cognitive ability[8,9,10] which has prompted researchers to identify which aspects of network structure can explain these behavioural variables[11,12,13,14,15,16]
We explore to what extent, if at all, node centrality measures can serve as a proxy for causal inference

Summary

Introduction

In the last two decades, network analysis has become increasingly popular across many disciplines dealing with a diverse range of social, biological, and information systems. Variables and their interactions are considered nodes and edges in a graph. Importance is confused with having causal influence This does not follow from the network paradigm (that is, not without additional effort through e.g. randomized trials), as it provides only a statistical representation of the underlying system, not a causal one; one might study how the system evolves over time and take the predictive performance of a node as its Granger-causal effect[25,26]. The absence of an edge between a pair of nodes (i.e., a partial correlation of zero) indicates that these nodes are conditionally independent, given the rest of the network Such networks, referred to as Markov random fields (MRFs)[31,32], capture only symmetric relationships. Other measures, such as closeness and betweenness of a node, are not directly based on a single node’s connection, but on shortest paths between nodes[34], or, such as eigenvector centrality, weigh the contributions from connections to nodes that are themselves central more heavily[35] (see Appendix for mathematical details)

Results

Discussion

Conclusion